In radio communications such as for example in the field of mobile wireless telecommunications, multiuser multiple-input and multiple-output (MU-MIMO) is a method for multiplying the capacity and spectral efficiency of a radio link using multiple transmit and/or receive antennas to exploit multipath propagation in order to serve more than one user on the same time-frequency resource block.
In its canonical form, large scale (Massive) MIMO system operates in time division duplex (TDD) mode, where the downlink and uplink transmissions are operating in the same frequency resource but are separated in time. The fact that physical propagation channels are reciprocal can be utilized in TDD operation [1]. Massive MIMO systems exploit the reciprocity to estimate the channel responses on the uplink and then use an acquired channel state information (CSI) for both uplink receive combining/detection and downlink transmit precoding/beamforming of the users' payload data. CSI may for example be acquired by transmitting predefined pilot signals and estimating the channel coefficients from the received signals [1]-[2]. An instantaneous channel matrix is acquired from the received pilot signal by applying an appropriate estimation technique. Channel estimation techniques such as the Bayesian minimum mean square error (MMSE) estimator and minimum-variance unbiased (MVU) estimator multiply the received pilot signal with an inverse of covariance matrices [3].
Theoretically, many antenna base stations promises manifold spectral capacity increase. This increase unfortunately comes at a cost of high processing complexity. In practical systems, given the lack of accurate knowledge of the channel and of the interference statistics, low computational complexity linear techniques such as conjugate match and zero forcing (ZF) have attracted large interest. Due to the inherent direct matrix inversion, polynomial expansion (PE) techniques have been utilized to further reduce ZF's computational complexity. These techniques readily lend themselves to trade-off between implementation complexity and performance.
Briefly stated, conventional techniques use mathematical operations with cubic order in computational complexity in the product of the number of antennas and the length of the pilot sequence. Therefore, the MMSE and MVU channel estimates oftentimes may not be calculated within an acceptable period of time. Moreover, the detection/precoding problem based on MMSE and ZF techniques is a mathematical operation with cubic computational complexity in the matrix dimension, which is equal to the number of users. In order to reduce such computational complexity one could resort to use polynomial expansion (PE) techniques [4]. PE approximates a matrix inversion by an L-degree matrix polynomial. The degree L is selected to balance between computational complexity and performance. If optimal coefficients are expensive to compute [4], some alternatives based on appropriate scaling [5] have been proposed. PE has been previously used in multiuser detection, where the decorrelating detector and the linear MMSE detector involve matrix inversions [6]. Recently, PE has also been used to reduce the precoding computational complexity in large-scale MIMO systems [7] where better performance was achieved by optimizing the matrix polynomials using asymptotic analysis.
Regardless, computational complexity is still important and known techniques used to reduce the amount of required calculations are relied on a trade-off between implementation complexity and performance Therefore, there is a need for improvements to reduce the amount of computational complexity in the determination of uplink receive combining/detection and downlink transmit precoding/beamforming parameters while limiting performance trade-offs.